A cyclic extension of the earthquake flow I

Abstract

Let T be Teichmüller space of a closed surface of genus at least 2. We describe an action of the circle on T x T, which limits to the earthquake flow when one of the parameters goes to a measured lamination in the Thurston boundary of T. This circle action shares some of the main properties of the earthquake flow, for instance it satisfies an extension of Thurston's Earthquake Theorem and it has a complex extension which is analogous and limits to complex earthquakes. Moreover, a related circle action on T x T extends to the product of two copies of the universal Teichmüller space.